Square Roots

In mathematics, a square root (√) of a number x is a number r such that r^2 = x, or, in other words, a number r whose square (the result of multiplying the number by itself, or r × r) is x.

Properties

The principal square root function

(usually just referred to as the "square root function") is a function that maps the set of non-negative real numbers onto itself. In geometrical terms, the square root function maps the area of a square to its side length.

The square root of x is rational if and only if x is a rational number that can be represented as a ratio of two perfect squares. (See square root of 2 for proofs that this is an irrational number, and quadratic irrational for a proof for all non-square natural numbers.) The square root function maps rational numbers into algebraic numbers (a superset of the rational numbers).


The graph of the function
, made up of half a parabola with a vertical directrix.



For all real numbers x



(see absolute value)


For all non-negative real numbers x and y,


and




The square root function is continuous for all non-negative x and differentiable for all positive x. If f denotes the square-root function, its derivative is given by:

The Taylor series of √1 + x about x = 0 converges for |x| <>

Reference:
http://en.wikipedia.org/wiki/Square_root